Two points are chosen at random in the interval [0, 1]; X denotes the first point chosen and Y denotes the second point chosen. Random variable U gives the type of triangle that can be formed from the three sub-intervals:

1. U = 0: the pieces do not form a triangle.
2. U = 1: the pieces form an obtuse triangle.
3. U = 2: the pieces form an acute triangle.

The first picture box shows the outcome of the experiment graphically. On each update, the cut points X and Y are shown as red dots, and the triangle is sketched when U = 1 or U = 2. The second picture box shows the sample space and the three events of interest:

1. U = 2 consists of the 2 interior regions.
2. U = 1 consists of the 6 middle regions.
3. U = 0 consists of the outer regions.

On each run, (X, Y) is shown as a red dot in the scatterplot, and is recorded in the first table on each update The probability density function of U is shown in blue in the graph box and is recorded in the graph table. On each update, the empirical density of U is shown in red in the graph box and is recorded in the graph table. Additionally, the value of U is recorded in the first table on each update.